Determine the coordinates of the absolute extrema for the curve

f(x) = x^2 - 4x + 1, on the interval 0 ≤ x ≤ 3

extrema occur when f'(x) = 0

f'(x) = 2x-4
now you can answer the question.

Of course, this is just a parabola, and you can find its vertex using Algebra I. No need for calculus...